Question

Question #eea8c

Answer 1

Choose `x` values (even numbers in this case) and work out a `y` value for each.
Draw a set of `x-y` axes and mark where the points are.

Explanation:

OK, let's take this step by step ....

1. You have an equation. (because there is an equal sign.)
   It needs to be solved, which means find values for the variables `x and y` which will make it true.

2. There is a problem! If it had ONE variable, like just `x`, it would be easy... If `3x +4 =25`, we can work out that `x =7`

BUT, there are TWO variables .....this means there are many, many values for `x` and `y` which will make this true.

`3" "` Find some values which work .... this means choose an `color(red)(x)`-value and work out a `color(blue)(y)` from the equation.

It will help to choose EVEN values of `x`, because we need to divide `x` by 2 and then multiply by `-3` and add `12`."

If `color(red)(x=6)` .... what is `color(blue)(y)`?

`y = -3/2 (color(red)(6))+12" "rarr" " y = color(blue)(+3)`

If `color(red)(x=10)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(10))+12" "rarr" " y = color(blue)(-3)`

If `color(red)(x=0)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(0))+12" "rarr" " y = color(blue)(12)`

If `color(red)(x=-8)` .... what is `color(blue)(y)`?
`y = -3/2 (color(red)(-8))+12" "rarr" " y = color(blue)(24)`

`4" "` So you can see that for ANY value you choose for `color(red)(x)` , you can find a matching `color(blue)(y)` answer.

So far we have the following pairs of values: `(color(red)(x,color(blue)(y)))`
`(color(red)(6),color(blue)(3))`, `(color(red)(10),color(blue)(-3))`, `(color(red)(0),color(blue)(12))`,`(color(red)(-8),color(blue)(24))`
You could do this over and over and over..

This step is often done in the form of a table.

`5" "` Plot points means: now that you have worked out matching pairs of `(x,y)` values, draw up a set of axes and plot the points on the grid.

The `x` is the first number and the `y` is the second.

If you plot (draw/mark) the points we have shown above, they will all lie in a straight line and you can draw a line (graph) through them. graph{y = -3/2x+12 [-15.42, 24.58, -5.36, 14.64]}